The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

Payment ($)   Probability
0                    .85
500                 .04
1000               .04
3000               .03
5000               .02
8000               .01
10000             .01

(a) Use the expected collision payment to determine the collision insurance premium that would enable the company to break even on the policy.

(b) The insurance company charges an annual rate of $520 for the collision insurance. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of the coverage). Why does a policyholder purchase a collision policy with this expected value?